Deck 10: Conics

Question 1

Write the standard form of the equation of the parabola with focus (4,5) and its vertex at (9,5).

A) $( x - 9 ) ^ { 2 } = 20 ( y - 5 )$
B) $( y - 5 ) ^ { 2 } = 20 ( x - 9 )$
C) $( x - 9 ) ^ { 2 } = - 20 ( y - 5 )$
D) $( x + 9 ) ^ { 2 } = 20 ( y + 5 )$
E) $( y - 5 ) ^ { 2 } = - 20 ( x - 9 )$

Answer 1

$( y - 5 ) ^ { 2 } = - 20 ( x - 9 )$

Question 2

Write the standard form of the equation of the circle with the center at (0,0) that has a radius of 6.

A) $y ^ { 2 } = 6 x ^ { 2 }$
B) $y ^ { 2 } = 36 x ^ { 2 }$
C) $x ^ { 2 } + y ^ { 2 } = 6$
D) $x ^ { 2 } + y ^ { 2 } = 36$
E) $y = 6 x ^ { 2 }$

Answer 2

$x ^ { 2 } + y ^ { 2 } = 36$

Question 3

Write the standard form of the equation of the circle with the center at (4,2) that has radius 4.

A) $( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 4$
B) $( x + 4 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 16$
C) $( x + 4 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 4$
D) $( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 16$
E) $( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 4$

Answer 3

$( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 16$

Question 4

Graph the equation $4 x ^ { 2 } + 4 y ^ { 2 } = 64$ .

A)
B)
C)
D)
E)

Question 5

Graph the equation $( x + 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 16$ .

A)
B)
C)
D)
E)

Question 6

Graph the equation $( x + 2 ) ^ { 2 } = - 3 ( y - 1 )$ .

A)
B)
C)
D)
E)

Question 7

Write the standard form of the equation of the circle with the center at (0,0) that passes through the point (6,2) .

A) $x ^ { 2 } + y ^ { 2 } = 8$
B) $x ^ { 2 } + y ^ { 2 } = 40$
C) $4 y ^ { 2 } = 36 x ^ { 2 }$
D) $36 y ^ { 2 } = 4 x ^ { 2 }$
E) $( x - 6 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 40$

Question 8

Identify the center and radius of the circle $x ^ { 2 } - 12 x + y ^ { 2 } - 6 y - 36 = 0$ .

A)center: (12,6) radius: 216
B)center: (-6,-3) radius: 9
C)center: (6,3) radius: 36
D)center: (6,3) radius: 9
E)center: (12,6) radius: 36

Question 9

Graph the equation $x ^ { 2 } = - 5 y$ .

A)
B)
C)
D)
E)

Question 10

Identify the center and radius of the circle $x ^ { 2 } + y ^ { 2 } = 25$ .

A)center: (1,1) radius: 25
B)center: (5,5) radius: 5
C)center: (0,0) radius: 5
D)center: (5,5) radius: 1
E)center: (0,0) radius: 25

Question 11

Identify the center and radius of the circle $( x - 2 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 81$ .

A)center: (-7,-2) radius: 9
B)center: (2,7) radius: 9
C)center: (2,7) radius: 81
D)center: (-2,-7) radius: 9
E)center: (7,2) radius: 81

Question 12

Graph the equation $( y - 1 ) ^ { 2 } = 5 ( x - 2 )$ .

A)
B)
C)
D)
E)

Question 13

Write the standard form of the equation of the circle with the center at (0,2) that passes through the point (7,3) .

A) $x ^ { 2 } + ( y + 2 ) ^ { 2 } = 50$
B) $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 58$
C) $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 50$
D) $( x - 2 ) ^ { 2 } + y ^ { 2 } = 58$
E) $( x + 2 ) ^ { 2 } + y ^ { 2 } = 50$

Question 14

Graph the equation $y ^ { 2 } = - 6 x$ .

A)
B)
C)
D)
E)

Question 15

Identify the center and radius of the circle $9 x ^ { 2 } + 9 y ^ { 2 } - 16 = 0$ .

A)center: (3,3) radius: 4
B)center: (0,0) radius: $\frac{4}{3}$
C)center: (0,0) radius: $\frac { 3 } { 4 }$
D)center: (0,4) radius: $\frac { 1 } { 3 }$
E)center: (0,4) radius: $\frac { 1 } { 9 }$

Question 16

Identify the center and radius of the circle $x ^ { 2 } + 18 x + y ^ { 2 } + 16 y + 45 = 0$ .

A)center: $( 18,16 )$ radius: 535
B)center: $( - 9 , - 8 )$ radius: 45
C)center: $( 9,8 )$ radius: 10
D)center: $( - 18 , - 16 )$ radius: 45
E)center: $( - 9 , - 8 )$ radius: 10

Question 17

Identify the center and radius of the circle $4 x ^ { 2 } + 4 y ^ { 2 } = 1$ .

A)center: (0,0) radius: $\frac { 1 } { 4 }$
B)center: (1,1) radius: 4
C)center: (1,1) radius: 2
D)center: (2,2) radius: 1
E)center: (0,0) radius: $\frac { 1 } { 2 }$

Question 18

Write the standard form of the equation of the parabola with focus (0,-2) and its vertex at the origin.

A) $y ^ { 2 } = 8 y$
B) $x ^ { 2 } = 8 x$
C) $y ^ { 2 } = - 8 x$
D) $x ^ { 2 } = - 8 y$
E) $x ^ { 2 } = \frac { 1 } { 8 } y$

Question 19

Write the standard form of the equation of the parabola with focus (-9,0) and its vertex at the origin.

A) $x ^ { 2 } = \frac { 1 } { 36 } y$
B) $y ^ { 2 } = 36 y$
C) $x ^ { 2 } = 36 x$
D) $x ^ { 2 } = - 36 y$
E) $y ^ { 2 } = - 36 x$

Question 20

Write the standard form of the equation of the parabola with focus (-5,5) and its vertex at (-5,8) .

A) $( y - 8 ) ^ { 2 } = - 3 ( x + 5 )$
B) $( y - 8 ) ^ { 2 } = 12 ( x + 5 )$
C) $( x + 5 ) ^ { 2 } = - 12 ( y - 8 )$
D) $( x + 5 ) ^ { 2 } = - 3 ( y - 8 )$
E) $( y - 8 ) ^ { 2 } = - 12 ( x + 5 )$

Question 21

Write the standard form of the equation of the ellipse centered at the origin. Vertices: $( - 6,0 ) ( 6,0 )$ Co-vertices: $( 0 , - 4 ) , ( 0,4 )$

A) $\frac { x ^ { 2 } } { 6 } = \frac { y ^ { 2 } } { 4 }$
B) $36 x ^ { 2 } + 16 y ^ { 2 } = 1$
C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 6 } = 1$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 36 } = 0$
E) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 16 } = 1$

Question 22

Write the standard form of the equation of the ellipse.

A) $\frac { x ^ { 2 } } { 4 } + \frac { 7 y ^ { 2 } } { 2 } = 1$
B) $4 x ^ { 2 } + 784 y ^ { 2 } = 64$
C) $\frac { x ^ { 2 } } { 16 } + \frac { 49 y ^ { 2 } } { 4 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { 2 y ^ { 2 } } { 7 } = 1$
E) $\frac { x ^ { 2 } } { 16 } + \frac { 4 y ^ { 2 } } { 49 } = 1$

Question 23

Write the standard form of the equation of the ellipse.

A) $\frac { ( x - 4 ) ^ { 2 } } { 2 } + \frac { ( y - 4 ) ^ { 2 } } { 3 } = 1$
B) $\frac { ( x - 4 ) ^ { 2 } } { 4 } + \frac { ( y - 4 ) ^ { 2 } } { 9 } = 1$
C) $\frac { ( x + 4 ) ^ { 2 } } { 4 } + \frac { ( y + 4 ) ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } + 4 } { 4 } + \frac { y ^ { 2 } + 4 } { 9 } = 1$
E) $\frac { ( x + 4 ) ^ { 2 } } { 4 } + \frac { ( y + 4 ) ^ { 2 } } { 6 } = 1$

Question 24

Write the standard form of the equation of the ellipse.

A) $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$
B) $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } + 2 } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$
D) $\frac { ( x - 2 ) ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 8 } = 1$
E) $\frac { ( x + 2 ) ^ { 2 } } { 3 } + \frac { y ^ { 2 } } { 4 } = 1$

Question 25

Identify the vertices and co-vertices of the ellipse $9 x ^ { 2 } + 49 y ^ { 2 } - 4 = 0$ .

A)vertices: $( - 3,0 ) , ( 3,0 )$ co-vertices: $( 0 , - 7 ) , ( 0,7 )$
B)vertices: $( 0 , - 7 ) , ( 0,7 )$ co-vertices: $( - 3,0 ) , ( 3,0 )$
C)vertices: $\left( - \frac { 3 } { 2 } , 0 \right) , \left( \frac { 3 } { 2 } , 0 \right)$ co-vertices: $\left( 0 , - \frac { 7 } { 2 } \right) , \left( 0 , \frac { 7 } { 2 } \right)$
D)vertices: $\left( - \frac { 2 } { 3 } , 0 \right) , \left( \frac { 2 } { 3 } , 0 \right)$ co-vertices: $\left( 0 , - \frac { 2 } { 7 } \right) , \left( 0 , \frac { 2 } { 7 } \right)$
E)vertices: $\left( 0 , - \frac { 2 } { 7 } \right) , \left( 0 , \frac { 2 } { 7 } \right)$ co-vertices: $\left( - \frac { 3 } { 2 } , 0 \right) , \left( \frac { 3 } { 2 } , 0 \right)$

Question 26

Identify the vertex and focus of the parabola $$x ^ { 2 } - 18 x + 24 y + 249 = 0$$ .

A)vertex: $( 9 , - 7 )$ focus: $( 105 , - 7 )$
B)vertex: $( - 9,7 )$ focus: $( - 105,7 )$
C)vertex: $( 9 , - 7 )$ focus: $( - 105 , - 7 )$
D)vertex: $( 9 , - 7 )$ focus: $( 9 , - 13 )$
E)vertex: $( - 9,7 )$ focus: $( - 9 , - 13 )$

Question 27

Identify the vertex and focus of the parabola $y ^ { 2 } = - 7 x$ .

A)vertex: (0,0) focus: $\left( - \frac { 7 } { 4 } , 0 \right)$
B)vertex: (0,0) focus: $\left( - \frac { 1 } { 7 } , 0 \right)$
C)vertex: (0,0) focus: (-7,0)
D)vertex: (0,0) focus: $\left( 0 , \frac { 7 } { 4 } \right)$
E)vertex: (0,0) focus: $\left( 0 , \frac { 1 } { 7 } \right)$

Question 28

Graph the function $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 1 } = 1$ .

A)
B)
C)
D)
E)

Question 29

Graph the function $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$ .

A)
B)
C)
D)
E)

Question 30

Identify the vertices and center of the ellipse $\frac { ( x - 5 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 49 } = 1$ .

A)vertices: $( 5 , - 7 ) , ( 5,7 )$ center: (5,2)
B)vertices: $( 3,2 ) , ( 3,2 )$ center: (5,2)
C)vertices: $( - 3,0 ) , ( 3,0 )$ center: (-5,-2)
D)vertices: $( - 5 , - 1 ) , ( 5,5 )$ center: (-5,-2)
E)vertices: $( 5 , - 5 ) , ( 5,9 )$ center: (5,2)

Question 31

Write the standard form of the equation of the ellipse.

A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$
B) $\frac { x ^ { 2 } } { 3 } + \frac { y ^ { 2 } } { 5 } = 1$
C) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$
D) $25 x ^ { 2 } + 9 y ^ { 2 } = 1$
E) $\frac { 9 x ^ { 2 } } { 25 } + \frac { 25 y ^ { 2 } } { 9 } = 1$

Question 32

Identify the vertex and focus of the parabola $$( x - 10 ) ^ { 2 } + 36 ( y + 6 ) = 0$$ .

A)vertex: $( 10 , - 6 )$ focus: $( - 154 , - 6 )$
B)vertex: $( 10 , - 6 )$ focus: $( 10 , - 15 )$
C)vertex: $( 10 , - 6 )$ focus: $( 154 , - 6 )$
D)vertex: $( - 10,6 )$ focus: $( - 10 , - 15 )$
E)vertex: $( - 10,6 )$ focus: $( - 154,6 )$

Question 33

A semicircular arch for a tunnel under a river has a diameter of 80 feet (see figure). Determine the height of the arch 4 feet from the edge of the tunnel.

A)36 feet
B) $12 \sqrt { 11 }$ feet
C) $4 \sqrt { 19 }$ feet
D) $4 \sqrt { 399 }$ feet
E) $6$ feet

Question 34

Identify the vertex and focus of the parabola $y = \frac { 1 } { 6 } x ^ { 2 }$ .

A)vertex: (0,0) focus: $\left( \frac { 3 } { 2 } , 0 \right)$
B)vertex: (0,0) focus: $\left( 0 , \frac { 2 } { 3 } \right)$
C)vertex: (0,0) focus: $\left( 0 , \frac { 3 } { 2 } \right)$
D)vertex: (0,0) focus: $\left( 0 , \frac { 1 } { 24 } \right)$
E)vertex: (0,0) focus: $\left( \frac { 2 } { 3 } , 0 \right)$

Question 35

Write the standard form of the equation of the ellipse centered at the origin, having a horizontal major axis of 6 units and a minor axis of 4 units.

A) $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 4 } = 1$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$
C) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 36 } = 1$
D) $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 18 } = 1$
E) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Question 36

Identify the vertices and co-vertices of the ellipse $25 x ^ { 2 } + 16 y ^ { 2 } - 9 = 0$ .

A)vertices: $\left( 0 , - \frac { 3 } { 4 } \right) , \left( 0 , \frac { 3 } { 4 } \right)$ co-vertices: $\left( - \frac { 3 } { 5 } , 0 \right) , \left( \frac { 3 } { 5 } , 0 \right)$
B)vertices: $\left( - \frac { 5 } { 3 } , 0 \right) , \left( \frac { 5 } { 3 } , 0 \right)$ co-vertices: $\left( 0 , - \frac { 4 } { 3 } \right) , \left( 0 , \frac { 4 } { 3 } \right)$
C)vertices: $\left( 0 , - \frac { 4 } { 3 } \right) , \left( 0 , \frac { 4 } { 3 } \right)$ co-vertices: $\left( - \frac { 5 } { 3 } , 0 \right) , \left( \frac { 5 } { 3 } , 0 \right)$
D)vertices: $( - 5,0 ) , ( 5,0 )$ co-vertices: $( 0 , - 4 ) , ( 0,4 )$
E)vertices: $( 0 , - 4 ) , ( 0,4 )$ co-vertices: $( - 5,0 ) , ( 5,0 )$

Question 37

Identify the vertices and co-vertices of the ellipse $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 1$ .

A)vertices: $( - 7,0 ) , ( 7,0 )$ co-vertices: $( 0 , - 2 ) , ( 0,2 )$
B)vertices: $( - 49,0 ) , ( 49,0 )$ co-vertices: $( 0 , - 4 ) , ( 0,4 )$
C)vertices: $( - 2,0 ) , ( 2,0 )$ co-vertices: $( 0 , - 7 ) , ( 0,7 )$
D)vertices: $( 0 , - 49 ) , ( 0,49 )$ co-vertices: $( - 4,0 ) , ( 4,0 )$
E)vertices: $( 0 , - 2 ) , ( 0,2 )$ co-vertices: $( - 7,0 ) , ( 7,0 )$

Question 38

Write the standard form of the equation of the ellipse centered at the origin, having a vertical 20 units and a minor axis of 10 units.

A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 100 } = 1$
B) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { x ^ { 2 } } { 50 } + \frac { y ^ { 2 } } { 200 } = 1$
D) $\frac { x ^ { 2 } } { 20 } + \frac { y ^ { 2 } } { 10 } = 1$
E) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 400 } = 1$

Question 39

Graph the function $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$ .

A)
B)
C)
D)
E)

Question 40

Graph the function $\frac { ( x + 2 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$ .

A)
B)
C)
D)
E)

Question 41

Write the standard form of the equation of the hyperbola centered at the origin. Vertices: $( 0 , - 3 ) , ( 0,3 )$ Asymptotes: $y = \frac { 1 } { 4 } x , y = - \frac { 1 } { 4 } x$

A) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1$
B) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 9 / 16 } = 1$
C) $( 0,10 ) \left( \frac { 3 } { 2 } , - \frac { 31 } { 4 } \right)$
D) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 144 } = 1$
E) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 144 } = 1$

Question 42

Identify the vertices and asymptotes of the hyperbola. $x ^ { 2 } - y ^ { 2 } = 36$

A)vertices: $( 6 , - 6 ) , ( 6,6 )$ asymptotes: $y = - 6 x , y = \frac { x } { 6 }$
B)vertices: $( - 36,0 ) , ( 36,0 )$ asymptotes: $y = - x , y = x$
C)vertices: $( 0 , - 6 ) , ( 0,6 )$ asymptotes: $y = - 6 x , y = \frac { x } { 6 }$
D)vertices: $( - 6,0 ) , ( 6,0 )$ asymptotes: $y = - x , y = x$
E)vertices: $( 0 , - 6 ) , ( 0,6 )$ asymptotes: $y = - x , y = x$

Question 43

Identify the vertices and asymptotes of the hyperbola. $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 81 } = 1$

A)vertices: $( - 5,0 ) , ( 5,0 )$ asymptotes: $y = - \frac { 5 } { 9 } x , y = \frac { 5 } { 9 } x$
B)vertices: $( - 5,0 ) , ( 5,0 )$ asymptotes: $y = - \frac { 9 } { 5 } x , y = \frac { 9 } { 5 } x$
C)vertices: $( 0 , - 9 ) , ( 0,9 )$ asymptotes: $y = - \frac { 5 } { 9 } x , y = \frac { 5 } { 9 } x$
D)vertices: $( - 9,0 ) , ( 9,0 )$ asymptotes: $y = - \frac { 9 } { 5 } x , y = \frac { 9 } { 5 } x$
E)vertices: $( - 9,0 ) , ( 9,0 )$ asymptotes: $y = - \frac { 5 } { 9 } x , y = \frac { 5 } { 9 } x$

Question 44

Graph the hyperbola. $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$

A)
B)
C)
D)
E)

Question 45

Write the standard form of the equation of the hyperbola centered at the origin. Vertices: $( - 2,0 ) , ( 2,0 )$ Asymptotes: $y = 5 x , y = - 5 x$

A) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 4 / 25 } = 1$
B) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 100 } = 1$
C) $\frac { x ^ { 2 } } { 4 / 25 } - \frac { y ^ { 2 } } { 4 } = 1$
D) $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 4 } = 1$
E) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 4 } = 1$

Question 46

Identify the vertices and asymptotes of the hyperbola. $y ^ { 2 } - x ^ { 2 } = 4$

A)vertices: $( 0 , - 2 ) , ( 0,2 )$ asymptotes: $y = - x , y = x$
B)vertices: $( - 4,0 ) , ( 4,0 )$ asymptotes: $y = - x , y = x$
C)vertices: $( - 2,0 ) , ( 2,0 )$ asymptotes: $y = - x , y = x$
D)vertices: $( - 2,2 ) , ( 2,2 )$ asymptotes: $y = - 2 x , y = \frac { x } { 2 }$
E)vertices: $( 0 , - 2 ) , ( 0,2 )$ asymptotes: $y = - 2 x , y = \frac { x } { 2 }$

Question 47

Graph the hyperbola. $x ^ { 2 } - y ^ { 2 } = 16$

A)
B)
C)
D)
E)

Question 48

Identify the vertices and asymptotes of the hyperbola. $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 100 } = 1$

A)vertices: $( - 10,0 ) , ( 10,0 )$ asymptotes: $y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x$
B)vertices: $( - 10,0 ) , ( 10,0 )$ asymptotes: $y = - \frac { 10 } { 7 } x , y = \frac { 10 } { 7 } x$
C)vertices: $( 0 , - 7 ) , ( 0,7 )$ asymptotes: $y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x$
D)vertices: $( 0 , - 10 ) , ( 0,10 )$ asymptotes: $y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x$
E)vertices: $( - 7,0 ) , ( 7,0 )$ asymptotes: $y = - \frac { 10 } { 7 } x , y = \frac { 10 } { 7 } x$

Question 49

Identify the vertices and center of the ellipse. $36 x ^ { 2 } + 25 y ^ { 2 } + 72 x - 200 y - 464 = 0$

A)vertices: $( - 6,4 ) , ( 4,4 )$ center: (-1,4)
B)vertices: $( - 1 , - 2 ) , ( - 1,10 )$ center: (-1,4)
C)vertices: $( - 7,4 ) , ( 5,4 )$ center: (-1,4)
D)vertices: $( 1 , - 1 ) , ( - 1,9 )$ center: (1,-4)
E)vertices: $( 1 , - 10 ) , ( - 1,2 )$ center: (1,-4)

Question 50

Graph the hyperbola. $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 36 } = 1$

A)
B)
C)
D)
E)

Question 51

A semielliptical arch for a tunnel under a river has a width of 80 feet and a height of 30 feet (see figure). Determine the height of the arch feet from the edge of the tunnel. Round your answer to one decimal place.

A) feet
B) feet
C) feet
D) feet
E) feet

Question 52

Write the standard form of the equation of the hyperbola centered at the origin. Vertices: $( 0 , - 2 ) , ( 0,2 )$ Asymptotes: $y = 4 x , y = - 4 x$

A) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 1 / 4 } = 1$
B) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 64 } = 1$
C) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 64 } = 1$
D) $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 4 } = 1$
E) $\frac { y ^ { 2 } } { 1 / 4 } - \frac { x ^ { 2 } } { 4 } = 1$

Question 53

Graph the hyperbola. $y ^ { 2 } - x ^ { 2 } = 36$

A)
B)
C)
D)
E)

Question 54

Identify the vertices and center of the ellipse. $25 ( x - 2 ) ^ { 2 } + 9 ( y + 6 ) ^ { 2 } = 4$

A)vertices: $\left( 2 , - \frac { 20 } { 3 } \right) , \left( 2 , \frac { 16 } { 3 } \right)$ center: (2,-6)
B)vertices: $\left( 2 , - \frac { 20 } { 3 } \right) , \left( 2 , - \frac { 16 } { 3 } \right)$ center: (2,-6)
C)vertices: $\left( 2 , \frac { 20 } { 3 } \right) , \left( 2 , \frac { 16 } { 3 } \right)$ center: (-2,6)
D)vertices: $\left( 2 , \frac { 20 } { 3 } \right) , \left( 2 , - \frac { 16 } { 3 } \right)$ center: (2,-6)
E)vertices: $\left( 2 , - \frac { 20 } { 3 } \right) , \left( 2 , - \frac { 16 } { 3 } \right)$ center: (-2,6)

Question 55

Sketch the graph of the equation. $\frac { ( x + 2 ) ^ { 2 } } { 25 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$

A)
B)
C)
D)
E)

Question 56

Sketch the graph of the equation. $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$

A)
B)
C)
D)
E)

Question 57

Identify the center and vertices of the hyperbola. $( y - 1 ) ^ { 2 } - ( x + 6 ) ^ { 2 } = 9$

A)center: $( - 6,1 )$ vertices: $( - 6 , - 2 ) , ( - 6,4 )$
B)center: $( 6 , - 1 )$ vertices: $( - 6,3 ) , ( - 6 , - 3 )$
C)center: $( 6 , - 1 )$ vertices: $( 3 , - 1 ) , ( 9 , - 1 )$
D)center: $( - 6,1 )$ vertices: $( - 9,1 ) , ( - 3,1 )$
E)center: $( - 6,1 )$ vertices: $( - 6,3 ) , ( - 6 , - 3 )$

Question 58

Sketch the graph of the equation. $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 4 } = 1$

A)
B)
C)
D)
E)

Question 59

Identify the vertices and center of the ellipse. $x ^ { 2 } + 36 y ^ { 2 } - 8 x - 72 y + 16 = 0$

A)vertices: $( - 5 , - 1 ) , ( 13 , - 1 )$ center: (-4,-1)
B)vertices: $( 3,1 ) , ( 5,1 )$ center: (4,1)
C)vertices: $( - 4 , - 7 ) , ( - 4,5 )$ center: $( - 4 , - 1 )$
D)vertices: $( - 2,1 ) , ( 10,1 )$ center: $( 4,1 )$
E)vertices: $( - 4 , - 2 ) , ( - 4,4 )$ center: $( - 4 , - 1 )$

Question 60

Identify the vertices and center of the ellipse. $25 x ^ { 2 } + 16 y ^ { 2 } - 100 x + 96 y - 156 = 0$

A)vertices: $( - 2 , - 2 ) , ( - 2,8 )$ center: (-2,3)
B)vertices: $( 2 , - 2 ) , ( 2,8 )$ center: (2,3)
C)vertices: $( 2 , - 8 ) , ( 2,2 )$ center: (2,-3)
D)vertices: $( - 2 , - 5 ) , ( - 2,5 )$ center: (-2,-3)
E)vertices: $( - 2 , - 5 ) , ( - 2,5 )$ center: (-2,3)

Question 61

Solve the system by the method of substitution. $$\left\{ \begin{aligned}x & = \sqrt { y + 10 } \\3 x + 2 y & = - 20\end{aligned} \right.$$

A) $( 0 , - 10 ) \left( - \frac { 3 } { 2 } , - \frac { 31 } { 4 } \right)$
B) $\left( \frac { 3 } { 2 } , - \frac { 31 } { 4 } \right)$
C) $( 0 , - 10 )$
D) $( 0,10 ) \left( \frac { 3 } { 2 } , - \frac { 31 } { 4 } \right)$
E)no solution exist

Question 62

Write the standard form of the equation of the hyperbola.

A) $\frac { ( y + 3 ) ^ { 2 } } { 9 } - \frac { ( x + 2 ) ^ { 2 } } { 36 } = 1$
B) $\frac { ( x - 2 ) ^ { 2 } } { 36 } - \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$
C) $\frac { ( y + 3 ) ^ { 2 } } { 36 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$
D) $\frac { ( y - 3 ) ^ { 2 } } { 36 } - \frac { ( x - 2 ) ^ { 2 } } { 9 } = 1$
E) $\frac { ( x + 2 ) ^ { 2 } } { 36 } - \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$

Question 63

Sketch the graph of the equation.

A) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 3 } = 1$
B) $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 36 } = 1$
D) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 9 } = 1$
E) $\frac { x ^ { 2 } } { 3 } - \frac { y ^ { 2 } } { 36 } = 1$

Question 64

Use a graphing calculator to graph the equations $\left\{ \begin{array} { c } x - 4 y = 1 \\\sqrt { x } - 1 = y\end{array} \right.$ and find the solutions of the system.

A) $( 0,1 ) ; ( 2,9 )$
B) $( 1,0 ) ; ( 4,1 )$
C) $( 4,0 ) ; ( 16,2 )$
D) $( 1,0 ) ; ( 9,2 )$
E) $( 0,4 ) ; ( 2,16 )$

Question 65

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $$\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 16 \\x - y = - 4\end{array} \right.$$

A) $( 0 , - 4 ) , ( - 4,0 )$
B) $( 0 , - 4 ) , ( 0,4 )$
C) $( 0,4 ) , ( 4,0 )$
D) $( 0,4 ) , ( - 4,0 )$
E)no solution exists

Question 66

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $$\left\{ \begin{array} { r } 2 x + y = 12 \\x ^ { 2 } + y ^ { 2 } = 36\end{array} \right.$$

A) $( 6,0 ) \left( - \frac { 18 } { 5 } , - \frac { 24 } { 5 } \right)$
B) $( - 6,0 ) \left( \frac { 18 } { 5 } , \frac { 24 } { 5 } \right)$
C) $( 6,0 ) \left( \frac { 18 } { 5 } , \frac { 24 } { 5 } \right)$
D) $( - 6,0 ) \left( - \frac { 18 } { 5 } , - \frac { 24 } { 5 } \right)$
E)no solution exists

Question 67

Sketch the graph of the equation.

A) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 3 } - \frac { y ^ { 2 } } { 36 } = 1$
C) $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 9 } = 1$
D) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 3 } = 1$
E) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 9 } = 1$

Question 68

Solve the system by the method of substitution. $$\left\{ \begin{array} { l } y = 2 x ^ { 2 } \\y = 38 x - 180\end{array} \right.$$

A) $( - 1,2 ) , ( 1,2 )$
B) $( 9,162 ) , ( 10,200 )$
C) $( - 9,162 ) , ( - 10,200 )$
D) $( 1,2 )$
E)no solution exists

Question 69

Solve the system by the method of substitution. $$\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\- 6 x + y = 5\end{array} \right.$$

A) $( 0,25 ) , ( - 30 , - 175 )$
B) $( 0,5 ) , ( 30,185 )$
C) $( 0,5 ) , \left( - \frac { 60 } { 37 } , - \frac { 175 } { 37 } \right)$
D) $( 0,25 ) , \left( - \frac { 60 } { 37 } , - \frac { 175 } { 37 } \right)$
E)no solution exists

Question 70

Identify the center and vertices of the hyperbola. $\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y + 6 ) ^ { 2 } } { 1 } = 1$

A)center: (2,-6) vertices: $( - 3 , - 6 ) , ( 7 , - 6 )$
B)center: (2,-6) vertices: $( 2 , - 7 ) , ( 2 , - 5 )$
C)center: (-2,6) vertices: $( - 2,1 ) , ( - 2,11 )$
D)center: (2,-6) vertices: $( 2 , - 11 ) , ( 2 , - 1 )$
E)center: $( - 2,6 )$ vertices: $( - 2,5 ) , ( - 2,7 )$

Question 71

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $$\left\{ \begin{array} { c } 9 x ^ { 2 } - 4 y ^ { 2 } = 36 \\8 x - 2 y = 0\end{array} \right.$$

A) $( 2 \sqrt { 3 } , 3 \sqrt { 2 } ) , ( - 2 \sqrt { 3 } , - 3 \sqrt { 2 } )$
B) $( 2,8 ) ( - 2 , - 8 )$
C) $( 2 \sqrt { 3 } , 3 \sqrt { 2 } )$
D) $( 2,8 )$
E)no solution exists

Question 72

Identify the center and vertices of the hyperbola. $x ^ { 2 } - 4 y ^ { 2 } + 40 y - 104 = 0$

A)center: (0,5) vertices: $( 0 , - 5 ) , ( 0,5 )$
B)center: (0,-5) vertices: $( - 2 , - 5 ) , ( 2 , - 5 )$
C)center: $( 0,5 )$ vertices: $( - 2,5 ) , ( 2,5 )$
D)center: $( 0 , - 5 )$ vertices: $( - 6 , - 5 ) , ( 6 , - 5 )$
E)center: $( 0 , - 5 )$ vertices: $( 0 , - 8 ) , ( 0 , - 2 )$

Question 73

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $$\left\{ \begin{array} { l } x - y ^ { 2 } = 0 \\x - y = - 10\end{array} \right.$$

A) $( 100,10 )$
B) $( 0 , - 10 )$
C) $( 10,0 )$
D) $\left( \frac { 19 + \sqrt { 41 } } { 2 } , \frac { - 1 + \sqrt { 41 } } { 2 } \right) , \left( \frac { 19 - \sqrt { 41 } } { 2 } , \frac { - 1 - \sqrt { 41 } } { 2 } \right)$
E)no solution exists

Question 74

Graph the equations to determine whether the system has any solutions. Find any solutions that exist. $$\left\{ \begin{array} { r } 3 x - y = 21 \\x ^ { 2 } - y ^ { 2 } = 49\end{array} \right.$$

A) $( - 7,0 ) \left( \frac { 28 } { 5 } , \frac { 21 } { 5 } \right)$
B) $( 7,0 ) \left( \frac { 35 } { 4 } , \frac { 21 } { 4 } \right)$
C) $( 0 , - 7 ) ( 28,7 )$
D) $( 0,7 ) ( - 7,42 )$
E)no solution exists

Question 75

Write the standard form of the equation of the hyperbola.

A) $\frac { ( x + 3 ) ^ { 2 } } { 4 } - \frac { ( y - 3 ) ^ { 2 } } { 16 / 5 } = 1$
B) $\frac { ( y - 3 ) ^ { 2 } } { 5 / 16 } - \frac { ( x + 3 ) ^ { 2 } } { 4 } = 1$
C) $\frac { ( y - 3 ) ^ { 2 } } { 4 } - \frac { ( x + 3 ) ^ { 2 } } { 5 / 16 } = 1$
D) $\frac { ( y + 3 ) ^ { 2 } } { 5 / 16 } - \frac { ( x - 3 ) ^ { 2 } } { 4 } = 1$
E) $\frac { ( x - 3 ) ^ { 2 } } { 4 } - \frac { ( y + 3 ) ^ { 2 } } { 16 / 5 } = 1$

Question 76

Solve the system by the method of substitution. $$\left\{ \begin{array} { l } x ^ { 2 } + y = 1 \\x + y = - 15\end{array} \right.$$

A) $\left( \frac { 1 - \sqrt { 65 } } { 2 } , \frac { - 31 - \sqrt { 65 } } { 2 } \right) , \left( \frac { 1 + \sqrt { 65 } } { 2 } , \frac { - 31 + \sqrt { 65 } } { 2 } \right)$
B) $\left( \frac { 1 - \sqrt { 65 } } { 2 } , \frac { - 31 + \sqrt { 65 } } { 2 } \right) , \left( \frac { 1 + \sqrt { 65 } } { 2 } , \frac { - 31 - \sqrt { 65 } } { 2 } \right)$
C) $\left( \frac { - 1 + \sqrt { 59 } } { 2 } , \frac { - 29 + \sqrt { 65 } } { 2 } \right) , \left( \frac { - 1 + \sqrt { 59 } } { 2 } , \frac { - 29 - \sqrt { 65 } } { 2 } \right)$
D) $\left( \frac { 1 - \sqrt { 59 } } { 2 } , \frac { - 29 + \sqrt { 65 } } { 2 } \right) , \left( \frac { 1 - \sqrt { 59 } } { 2 } , \frac { - 29 - \sqrt { 65 } } { 2 } \right)$
E)no solution exists

Question 77

Solve the system by the method of substitution. $$\left\{ \begin{array} { l } x ^ { 2 } - y = - 6 \\8 x - y = 6\end{array} \right.$$

A) $( 2,42 )$
B) $( 6,30 )$
C) $( 6,30 ) , ( 2,42 )$
D) $( 6,42 ) , ( 2,10 )$
E)no solution exists

Question 78

Solve the system by the method of substitution. $$\left\{ \begin{aligned}y & = x ^ { 2 } - 2 \\7 x + 2 y & = - 4\end{aligned} \right.$$

A) $( 0 , - 2 ) \left( - \frac { 7 } { 2 } , \frac { 41 } { 4 } \right)$
B) $( 0 , - 2 ) \left( \frac { 7 } { 2 } , \frac { 41 } { 4 } \right)$
C) $\left( - \frac { 7 } { 2 } , \frac { 41 } { 4 } \right)$
D) $( 0,2 ) \left( - \frac { 7 } { 2 } , \frac { 41 } { 4 } \right)$
E)no solution exists

Question 79

Identify the center and vertices of the hyperbola. $x ^ { 2 } - 16 y ^ { 2 } - 10 x - 96 y - 135 = 0$

A)center: (5,-3) vertices: $( 1 , - 3 ) , ( 9 , - 3 )$
B)center: (-5,3) vertices: $( - 5,2 ) , ( - 5,4 )$
C)center: $( - 10,10 )$ vertices: $( - 10,2 ) , ( - 10,10 )$
D)center: $( 5 , - 3 )$ vertices: $( 5 , - 4 ) , ( 5 , - 2 )$
E)center: $( 10 , - 10 )$ vertices: $( 10,24 ) , ( 10 , - 24 )$

Question 80

Solve the system by the method of substitution. $$\left\{ \begin{array} { l } x - y ^ { 2 } = 0 \\x - y = 42\end{array} \right.$$

A) $( 36,6 ) , ( 25 , - 5 )$
B) $( 36 , - 6 ) , ( 25,5 )$
C) $( 36,6 ) , ( 49 , - 7 )$
D) $( 36 , - 6 ) , ( 49,7 )$
E)no solution exists